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Minimal gravitational coupling in the Newtonian theory and the covariant Schrödinger equation

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Abstract

The role of the Bargmann group (11-dimensional extended Galilei group) in nonrelativistic gravitation theory is investigated. The generalized Newtonian gravitation theory (Newton-Cartan theory) achieves the status of a gauge theory about as much as general relativity and couples minimally to a complex scalar field leading to a four-dimensionally covariant Schrödinger equation. Matter current and stress-energy tensor follow correctly from the Lagrangian. This theory on curved Newtonian space-time is also shown to be a limit of the Einstein-Klein-Gordon theory.

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Author notes

  1. H. P. Künzle

    Present address: Department of Mathematics, University of Alberta, T6G 2G1, Edmonton, Canada

Authors and Affiliations

  1. Centre de Physique Théorique, C.N.R.S. Luminy, Case 907, 13288, Marseille, France

    C. Duval & H. P. Künzle

  2. Faculté des Sciences de Luminy et Centre de Physique Théorique, C.N.R.S., 70 Route Léon Lachamp, Case 907, F. 13288, Marseille Cedex 9

    C. Duval

  3. Institut für Astrophysik, Max-Planck-Institut für Physik und Astrophysik, D. 8046, Garching bei München, Germany

    H. P. Künzle

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Partially supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. A8059.

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Duval, C., Künzle, H.P. Minimal gravitational coupling in the Newtonian theory and the covariant Schrödinger equation. Gen Relat Gravit 16, 333–347 (1984). https://doi.org/10.1007/BF00762191

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  • DOI: https://doi.org/10.1007/BF00762191

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